What is the solution for f^'(x)=(x^2)/(x+1) ?

The solution for f^'(x)=(x^2)/(x+1) is f(x)=((x+1)^2)/2-2(x+1)+ln(x+1)+c_{1}

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f^'(x)=(x^2)/(x+1)

f^{^{'}} (x) = \frac{x ^{2}}{x + 1}

f (x) = \frac{( x + 1 ) ^{2}}{2} - 2 (x + 1) + ln (x + 1) + c_{1}

Solution steps

f^{'} (x) = \frac{x ^{2}}{x + 1}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

f (x) = \int \frac{x ^{2}}{x + 1} d x

\int \frac{x ^{2}}{x + 1} d x = \frac{( x + 1 ) ^{2}}{2} - 2 (x + 1) + ln (x + 1) + c_{1}

f (x) = \frac{( x + 1 ) ^{2}}{2} - 2 (x + 1) + ln (x + 1) + c_{1}

(- 4, 1), (- 7, - 5)

\frac{d}{d x} ((x - \frac{1}{x ^{2}})^{5})

x y + \frac{d y}{d x} = 120 x

\int ln (6 - 3 x) d x

2 y^{^{''}} - 5 y^{^{'}} + 6 y = 0

What is the solution for f^'(x)=(x^2)/(x+1) ?
The solution for f^'(x)=(x^2)/(x+1) is f(x)=((x+1)^2)/2-2(x+1)+ln(x+1)+c_{1}